Estimating the complier average causal effect in generalized additive partial linear models using likelihood analysis

In a nonrandomized binary treatment and covariates setting, we aim to model the complier average causal effect using generalized additive partial linear models. Under the assumption of principal ignorability, we predict latent principal strata using covariates and construct estimators for unknown parameters and functions by expanding them as linear combinations of polynomial spline functions within a likelihood-based framework. Simulation studies have shown that the suggested inference procedure performs effectively across various scenarios. We have applied this method to analyze the household income dataset obtained from the Chinese Household Income Project Survey in 2013.